A double-wishbone suspension locates its upright with upper and lower A-arms. This calculator solves a stated front-view geometry: both arms start horizontal, the upright starts vertical, and the chassis pivots remain fixed. The drawing uses the same rigid links as the calculation.
Double Wishbone Suspension Interactive Calculator
Compare rigid wishbones in a defined geometry: horizontal arms and vertical upright at zero bump. Enter front-view reaches and lower ball-joint travel. The wheel and arms follow the calculated positions.
Equation Used
- Both wishbone front-view reaches start horizontal; upright starts vertical.
- Parallel fore-aft chassis axes and rigid arms/upright.
- Bump input is lower ball-joint rise, not wheel-centre travel.
- Wheel offset 70 mm, diameter 500 mm and coilover are illustrative.
- No steering, caster, toe, tyre contact, loads or compliance.
One fixed-chassis corner. Front-view kinematics with illustrative wheel and spring dimensions; no force or handling prediction.
Two A-arms locate one upright
Each wishbone has two chassis attachments along a fore-aft axis and one outer ball joint. The upright joins the upper and lower ball joints and carries the wheel. As the lower ball joint rises, its arm swings about the fixed chassis axis. The upper ball joint must simultaneously stay on the upper arm’s circle and remain one upright length from the lower joint.
The oblique drawing makes the two legs of each A-arm visible. Its camber geometry is solved in the front view with parallel fore-aft pivot axes. The displayed spring-damper follows a lower-arm mounting point, but no spring force is calculated.
Compare a defined suspension geometry
Change the front-view upper and lower reaches, the upright’s ball-joint gap and the lower-joint bump. The results show camber, its local rate at the selected bump, and wheel-centre vertical and lateral movement.
The arm inputs are the distance from each chassis pivot axis to its ball joint in the front view. They are not the longer diagonal legs of an A-shaped arm. The travel input refers specifically to the lower ball joint; the wheel centre moves by a different amount.
Changing an arm reach also repositions its chassis pivot so the zero-bump arms remain horizontal and the upright remains vertical. This is a family of defined geometries, not a fit to arbitrary vehicle hardpoints.
Rigid-link closure and camber
Use x positive outward from the chassis and y positive upward. Let upper reach=a, lower reach=b, and ball-joint gap=h, all in millimetres. The lower chassis pivot is O=(0,0), and the upper pivot is U=(b−a,h). At zero bump the lower and upper ball joints are B=(b,0) and C=(b,h).
For entered lower-joint bump z, B=(sqrt(b²−z²),z). Solve |C−U|=a and |C−B|=h using the circle-intersection branch continuous from the zero-bump pose. This keeps both wishbones and the upright rigid.
Camber γ=atan2(Cx−Bx,Cy−By), converted to degrees. A negative value means the top of the wheel tilts toward the chassis. The local rate is dγ/dz in degrees per millimetre of lower-joint bump; it is the tangent slope at the selected position, not the total camber divided by travel.
For the wheel-centre outputs, let u=(C−B)/h and outward normal n=(uy,−ux). The model uses W=(B+C)/2+70n. Rise and outward shift are Wy(z)−Wy(0) and Wx(z)−Wx(0). The 70 mm offset is a stated illustration dimension.
What the controls change
With equal upper and lower front-view reaches, the linkage becomes a parallelogram and the upright stays vertical. Camber remains zero through the modelled bump, although the wheel moves inward as the arms swing.
With unequal reaches, the two outer joints follow different circles and the upright tilts. The amount depends on the upright spacing and bump as well as the two reaches. At the horizontal-arm starting pose, the instantaneous camber rate is zero; that does not mean camber remains zero later in the travel.
Select zero bump to inspect the starting geometry. The animation stops at that pose and all displacement outputs return to zero.
Model boundaries
This is one fixed-chassis corner with rigid links, parallel fore-aft pivot axes and no steering. The wheel diameter, 70 mm wheel offset, wishbone widths and spring-damper mounting are illustrative. They are not a particular vehicle’s dimensions.
The model does not include caster, toe, chassis roll, tyre contact, bushing compliance, spring force, damping, braking or cornering loads. It cannot predict handling, tyre wear, grip or component strength.
Real suspension analysis requires measured hardpoints and the relevant load cases. The two front-view arm reaches, upright spacing and lower-joint bump together determine the wheel position in the stated starting geometry.
Double-wishbone calculator questions
Why are the arm lengths measured in the front view?
The calculation treats each wishbone as rotation about its fore-aft chassis axis. Its front-view reach is the radius to the ball joint. Each diagonal A-arm leg is longer because its chassis attachment is fore or aft of the ball joint.
Is bump the wheel-centre movement?
No. It is the lower ball-joint rise. The separate wheel-centre rise output accounts for the upright rotation and the stated wheel offset.
What does negative camber mean?
The wheel’s top tilts inward, toward the chassis.
Why does the local rate change during bump?
The links trace circles, so their relative movement is nonlinear. Local rate is the derivative at the selected bump, not a constant gain for the whole stroke.
Can this identify the best handling setup?
No. It compares the stated kinematic geometry without tyre, chassis or load behaviour.
Reference and calculation basis
MathWorks: Double Wishbone Suspension provides a multibody example of the suspension type. This page uses its own simplified, explicitly specified single-corner geometry; it does not reproduce that model’s dimensions or dynamics. The equations above follow directly from fixed link lengths and circle intersections.
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